This paper documents a model of the COVID-19 epidemic in Canada. Mobility data is used to model the reproduction number of the COVID-19 epidemic over time using a Bayesian hierarchical model. This is achieved by adapting the work by Imperial College London researchers [1] for Canada. Authors from Imperial College London have built similar models for Brazil [2] and the United States [3]. In this case the model is calibrated to reported COVID-19 deaths as compiled in [4].
The model uses mobility movement indexes by province produced by Google [5]. Furthermore the model includes an effect for mandatory indoor mask-wearing based on data as compiled in [6] (and extended).
The model and report are automatically generated on a regular basis using R [7]. This version contains data available on 03 November 2020.
An online, regularly updated version of this report is available here.
As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using git. The git commit hash for this project at the time of generating this paper was 757161015e0851db196bfee02148db6390920d06 and this change was made on 2020-11-03.
2020-11-01
A detailed description of the methodology and assumptions is provided below below. The key features of the approach employed are summarised here:
The national mobility data from [5] is plotted below. The model uses the indexes at a provincial level but here the national indexes are plotted for convenience. Clear trends are observable.
Google Mobility Indexes for Canada
The chart below summarises the average mobility index used in the model. This is the average of mobility indicators excluding parks and residential. This follows [8].
Average Mobility
The average mobility (excluding residential & park indexes) is plotted below for the various provinces. Grouped provinces uses mobility weighted by the population of provinces where there is mobility data available.
Average Mobility by Province
Mandatory mask-wearing mandates are compiled by province in [6]. This data contains a single indicator by province with 0 indicating no mandate and 1 indicating a province wide mandate. The authors also used numbers between 0 and 1 to indicate mandates that affected only subsets of the population.
The grouped provinces use a weighted average (by population) of the mask-wearing indicator from the respective provinces.
Mandatory Indoor Mask-Wearing by Province
The sections below show how well the model is reproducing past data. Various panels are plotted for each province:
In all the charts the darker shaded area represents a confidence interval of 50% and the lighter shaded area represents a confidence interval of 95%.
The reported deaths (in brown) and estimated deaths (in blue) are plotted below. The calibration appears reasonable.
Projected Deaths compared to Reported COVID-19 Deaths in Alberta
Below modelled infections are plotted compared to confirmed cases. Over the last 14 days it would appear that 60.8% of all new infections were tested.
Projected Infections compared to Confirmed Cases in Alberta
Below the \(R_{t,m}\) is plotted.
Effective Reproduction Number in Alberta
Below the \(-\epsilon_{w_m(t),m}\) is plotted.
Weekly AR(2) Effect Plot for Alberta
The reported deaths (in brown) and estimated deaths (in blue) are plotted below. The calibration appears reasonable.
Projected Deaths compared to Reported COVID-19 Deaths in British Columbia
Below modelled infections are plotted compared to confirmed cases. Over the last 14 days it would appear that there were 335% reported cases vs. modelled infections. This indicates that the model is under-estimating the epidemic in this province as measured by cases. It may be that the recent growth in cases is yet to result in increased deaths.
Projected Infections compared to Confirmed Cases in British Columbia
Below the \(R_{t,m}\) is plotted.
Effective Reproduction Number in British Columbia
Below the \(-\epsilon_{w_m(t),m}\) is plotted.
Weekly AR(2) Effect Plot for British Columbia
The reported deaths (in brown) and estimated deaths (in blue) are plotted below. Reported deaths are still low but rising.
Projected Deaths compared to Reported COVID-19 Deaths in Manitoba
Below modelled infections are plotted compared to confirmed cases. Over the last 14 days it would appear that 24.5% of all new infections were tested.
Projected Infections compared to Confirmed Cases in Manitoba
Below the \(R_{t,m}\) is plotted.
Effective Reproduction Number in Manitoba
Below the \(-\epsilon_{w_m(t),m}\) is plotted.
Weekly AR(2) Effect Plot for Manitoba
The reported deaths (in brown) and estimated deaths (in blue) are plotted below. There are limited recently reported deaths.
Projected Deaths compared to Reported COVID-19 Deaths in Ontario
Below modelled infections are plotted compared to confirmed cases. Over the last 14 days it would appear that 5.8% of all new infections were tested.
Projected Infections compared to Confirmed Cases in Maritime Provinces
Below the \(R_{t,m}\) is plotted.
Effective Reproduction Number in Maritime Provinces
Below the \(-\epsilon_{w_m(t),m}\) is plotted.
Weekly AR(2) Effect Plot for Maritime Provinces
The reported deaths (in brown) and estimated deaths (in blue) are plotted below. The calibration appears reasonable.
Projected Deaths compared to Reported COVID-19 Deaths in Ontario
Below modelled infections are plotted compared to confirmed cases. Over the last 14 days it would appear that 87.3% of all new infections were tested.
Projected Infections compared to Confirmed Cases in Ontario
Below the \(R_{t,m}\) is plotted.
Effective Reproduction Number in Ontario
Below the \(-\epsilon_{w_m(t),m}\) is plotted.
Weekly AR(2) Effect Plot for Ontario
The reported deaths (in brown) and estimated deaths (in blue) are plotted below. The calibration appears reasonable.
Projected Deaths compared to Reported COVID-19 Deaths in Quebec
Below modelled infections are plotted compared to confirmed cases. Over the last 14 days it would appear that 34.2% of all new infections were tested.
Projected Infections compared to Confirmed Cases in Quebec
Below the \(R_{t,m}\) is plotted.
Effective Reproduction Number in Quebec
Below the \(-\epsilon_{w_m(t),m}\) is plotted.
Weekly AR(2) Effect Plot for Quebec
The reported deaths (in brown) and estimated deaths (in blue) are plotted below. There are somewhat limited reported deaths for this province.
Projected Deaths compared to Reported COVID-19 Deaths in Saskatchewan
Below modelled infections are plotted compared to confirmed cases. Over the last 14 days it would appear that there were 1124.8% reported cases vs. modelled infections. This indicates that the model is under-estimating the epidemic in this province as measured by cases. From the data it’s clear that the cases are growing but deaths have not yet increased.
Projected Infections compared to Confirmed Cases in Saskatchewan
Below the \(R_{t,m}\) is plotted.
Effective Reproduction Number in Saskatchewan
Below the \(-\epsilon_{w_m(t),m}\) is plotted.
Weekly AR(2) Effect Plot for Saskatchewan
To understand the net parameter estimates for \(\alpha\) and \(\alpha_{m}^s\) and their impact on \(R_{t,m}\) the percentage reduction in \(R_{t,m}\) is plotted below. The plot is made assuming the particular index is 1 (representing a 100% reduction in average mobility).
This is equivalent to plotting \(1-2\cdot\phi^{-1}(-(\alpha+\alpha_{m}^s))\) for a particular province \(m\). \(1-2\cdot\phi^{-1}(-(\beta+\beta_{m}^s))\) is also plotted.
Model Parameter Estimates with 95% Confidence Intervals
Estimates for \(R_{0,m}\) for each province are plotted below. It should be noted that the provinces with low \(R_{0,m}\) tend to be the ones with less data early in the epidemic. This indicates that \(R_{0,m}\) may not be correctly estimated for these provinces as there is no data to differentiate it from post lockdown \(R_{t,m}\). This may be the cause for the limited impact of mobility for these provinces.
In any case, for all provinces, it is probable that the posterior estimates for \(R_{0,m}\) are not heavily influenced by the data. This is probably due to the relatively early lockdown implemented in Canada. There were probably not enough deaths that resulted from infection prior to lockdown to develop an independent estimate for each province of \(R_{0,m}\).
Initial Reproduction Number by Province
Current estimates and 95% confidence intervals for \(R_{t,m}\) (current effective reproduction number) are plotted below for each province. A value below 1 would indicate an epidemic that is slowing while a value above 1 indicates an epidemic that is growing. It is clear that the spread of the epidemic is somewhat slowed compared to the initial \(R_{0,m}\). For some provinces the confidence interval does not include 1 which would indicate this to a stronger degree.
Current Reproduction Number by Province
The estimated attack rate (with 95% confidence intervals) is tabulated below. This is the proportion of the population infected to date. This figure has to be estimated, because many that are infected experience no or mild symptoms, thus they may not seek medical advice and hence will never be tested. The confidence intervals for these estimates remain wide. The highest attack rates are occurring in Quebec and Ontario.
| Province | Attack Rate |
|---|---|
| Alberta | 1.3% [0.9%-1.8%] |
| British Columbia | 0.5% [0.4%-0.7%] |
| Manitoba | 1.6% [0.8%-3.1%] |
| Maritime Provinces | 0.3% [0.2%-0.5%] |
| Ontario | 2.4% [1.9%-3.1%] |
| Quebec | 7.8% [6.2%-10.0%] |
| Saskatchewan | 0.2% [0.1%-0.3%] |
| Canada | 3.0% [2.6%-3.6%] |
One of the reasons we build models is so that we can make sense of the future or indeed the past. We can project forward models to assess the impact of varying assumptions on future outcomes. This gives us a sense of how changes in actions may impact the future. I.e. it allows us to answer “what if” questions. Note however that in projecting the future we are extrapolating, and due care needs to be taken. There are numerous limitations to this model and these projections dicussed below but the author is also of the opinion that the projections add value in that they indicate a significant range across the scenarios projected and in such a manner inform discussion.
All models are wrong but some are useful - George Box [9]
An incorrect model can be useful because it enables a better understanding of the model and the phenomena being modelled. This section should be used with caution because, as we show in calibration, the model seems to be projecting higher deaths than observed for some provinces.
Note detailed projection output can be found here.
Projections are done using constant, increasing and decreasing mobility but other interventions are left constant. It should also be noted that the \(\epsilon_{w_m(t),m}\) are projected forward at constant levels and are not adjusted for projection purposes.
The \(\epsilon_{w_m(t),m}\) is held at “current” levels when projecting forwards. It should be noted that these levels are set 28 days prior as recent deaths only affect infections that occured prior to that. Based on the observed calibration for Western Cape there is a possibility that this may be resulting in too low recent infections.
In this projection mobility is held constant at current levels. Level 4 interventions are left intact.
The result of this scenario as at 31 December 2020 is tabulated below. Note based on these it would appear that some provinces have already reached the peak in daily deaths.
| Province | Attack Rate | Deaths | Peak Daily Deaths | Peak Date |
|---|---|---|---|---|
| Alberta | 9.6% [1.2%-49.3%] | 1 402 [ 370- 6 091] | 103 | 2021-02-06 |
| British Columbia | 0.8% [0.4%-2.3%] | 327 [ 245- 624] | 17 | 2021-04-15 |
| Manitoba | 21.9% [1.7%-65.1%] | 1 305 [ 165- 4 537] | 58 | 2021-01-15 |
| Maritime Provinces | 8.3% [0.2%-70.7%] | 700 [ 65- 5 914] | 97 | 2021-02-05 |
| Ontario | 4.0% [2.1%-12.7%] | 4 282 [ 3 169- 8 130] | 152 | 2021-03-12 |
| Quebec | 14.8% [7.1%-39.1%] | 9 731 [ 6 604-18 984] | 182 | 2021-02-04 |
| Saskatchewan | 0.9% [0.1%-4.8%] | 43 [ 12- 133] | 6 | 2021-03-08 |
| Canada | 10.1% [5.1%-20.5%] | 17 790 [12 385-29 946] | 560 | 2021-02-11 |
This scenario assumes future mobility half-way between current mobility levels and normal levels. Other interventions are left intact. The attack rate and deaths after increasing mobility are tabulated below (as at 31 December 2020).
| Province | Attack Rate | Deaths | Peak Daily Deaths | Peak Date |
|---|---|---|---|---|
| Alberta | 26.3% [1.4%-81.5%] | 3 198 [ 408-13 833] | 254 | 2021-01-20 |
| British Columbia | 1.4% [0.5%-7.4%] | 396 [ 247- 1 146] | 63 | 2021-03-19 |
| Manitoba | 32.2% [2.4%-76.4%] | 1 849 [ 202- 5 961] | 87 | 2021-01-11 |
| Maritime Provinces | 9.6% [0.2%-75.9%] | 803 [ 65- 6 936] | 109 | 2021-02-03 |
| Ontario | 9.2% [2.2%-46.0%] | 6 077 [ 3 267-19 315] | 565 | 2021-02-15 |
| Quebec | 27.0% [8.1%-69.4%] | 13 582 [ 6 955-33 914] | 498 | 2021-01-22 |
| Saskatchewan | 1.4% [0.1%-11.5%] | 54 [ 12- 244] | 9 | 2021-02-25 |
| Canada | 19.9% [7.6%-42.7%] | 25 959 [14 370-50 828] | 1 448 | 2021-01-30 |
Based on the above an increase mobility could mean roughly 8 000 more deaths by the end of the year.
This scenario assumes future mobility is decreased by 50% more than currently. The attack rate and deaths after decreased mobility are tabulated below (as at 31 December 2020).
| Province | Attack Rate | Deaths | Peak Daily Deaths | Peak Date |
|---|---|---|---|---|
| Alberta | 3.9% [1.0%-19.4%] | 801 [ 353- 2 748] | 27 | 2021-02-13 |
| British Columbia | 0.6% [0.4%-1.2%] | 303 [ 243- 452] | 3 | 2020-04-11 |
| Manitoba | 14.8% [1.3%-55.0%] | 953 [ 142- 3 509] | 36 | 2021-01-17 |
| Maritime Provinces | 7.1% [0.2%-65.2%] | 613 [ 64- 4 914] | 85 | 2021-02-07 |
| Ontario | 2.9% [2.0%-5.4%] | 3 776 [ 3 117- 5 443] | 57 | 2020-04-28 |
| Quebec | 10.4% [6.7%-21.3%] | 8 253 [ 6 431-13 137] | 108 | 2020-05-02 |
| Saskatchewan | 0.6% [0.1%-2.7%] | 35 [ 12- 94] | 3 | 2021-03-14 |
| Canada | 6.8% [4.2%-13.1%] | 14 735 [11 500-22 446] | 209 | 2021-02-05 |
Based on the above a decrease in mobility could mean roughly 3 000 fewer deaths by the end of the year.
We plot below the results for Canada as a whole. This is the sum of the provincial projections.
Projected Attack Rate and Daily Deaths in Canada
The attack rate and deaths over a longer period for both the constant mobility and increased mobility scenarios are plotted below:
Projected Attack Rate and Daily Deaths in Canada by Scenario
Below we plot the projections for Alberta.
Projected Attack Rate and Daily Deaths in Alberta
The attack rate and deaths over a longer period for both the constant mobility and increased mobility scenarios are plotted below:
Projected Attack Rate and Daily Deaths in Alberta by Scenario
Below we plot the projections for the British Columbia.
Projected Attack Rate and Daily Deaths in British Columbia
The attack rate and deaths over a longer period for both the constant mobility and increased mobility scenarios are plotted below:
Projected Attack Rate and Daily Deaths in British Columbia by Scenario
Below we plot the projections for Manitoba
Projected Attack Rate and Daily Deaths in Manitoba
The attack rate and deaths over a longer period for both the constant mobility and increased mobility scenarios are plotted below:
Projected Attack Rate and Daily Deaths in Manitoba by Scenario
Below we plot the projections for Maritime Provinces
Projected Attack Rate and Daily Deaths in Maritime Provinces
The attack rate and deaths over a longer period for both the constant mobility and increased mobility scenarios are plotted below:
Projected Attack Rate and Daily Deaths in Maritime Provinces by Scenario
Below we plot the projections for Ontario.
Projected Attack Rate and Daily Deaths in Ontario
The attack rate and deaths over a longer period for both the constant mobility and increased mobility scenarios are plotted below:
Projected Attack Rate and Daily Deaths in Ontario by Scenario
Below we plot the projections for Quebec.
Projected Attack Rate and Daily Deaths in Quebec
The attack rate and deaths over a longer period for both the constant mobility and increased mobility scenarios are plotted below:
Projected Attack Rate and Daily Deaths in Quebec by Scenario
Below we plot the projections for Saskatchewan.
Projected Attack Rate and Daily Deaths in Saskatchewan
The attack rate and deaths over a longer period for both the constant mobility and increased mobility scenarios are plotted below:
Projected Attack Rate and Daily Deaths in Saskatchewan by Scenario
There remains significant uncertainty with all matters relating this epidemic. This includes uncertainty in data, assumptions and many epidemiological and medical matters relating to this disease. It is therefore likely that the model will not be accurate. It is also reflected in the wide confidence intervals of many of the results of the model.
Some researchers have gone as far as to say that it is not possible to accurately estimate the mean number of fatalities of pandemics based on data ([10] & [11]). This would indicate the goal of the paper may be futile.
This paper has however attempted to allow for uncertainty using the Bayesian approach here which results in at least some distribution of possible results, some of which are definitely catastrophic and some of which are less severe.
This analysis has various limitations. We highlight a few below but there are many. Perhaps the most important being the lack of good quality data.
In Europe the lockdowns have been able to reduce \(R_{t}\) below 1 for various countries [16]. From the results it’s clear that \(R_{t,m}\) in most provinces has reduced from the starting values of \(R_{0,m}\) and this has slowed the spread of the epidemic in Canada saving lives.
Based on the modelling increased mobility it is expected to result in roughly 0 more deaths by the end of the year. This ignores other impacts such as ICU availability and the impact on deaths from other causes which would be expected to increase these figures, but also the impact of the homogeneity assumption which might be exacerbating this number.
Reducing mobility could result in roughly NA fewer deaths by the end of the year.
The IFR is not treated as a parameter but as a constant with random noise. Changes to the IFR will change the modelled infections that correlate with the observed deaths. Sensitivity to the IFR could be modelled.
If the IFR is higher than what is assumed (which would seem likely), we would expect lower attack rates at present and thus the epidemic could result in a higher ultimate death toll as well. A lower than assumed IFR would imply more people have been infected already and we would be further along in the epidemic.
Using mobility data is useful not only to measure the impact of government interventions but also to include the societal response to those interventions (as they affect mobility). This means that changes in the reaction to new regulations can be modelled. It may also be useful going forward as many new regulations are introduced possibly at a provincial level to summarise the impact of interventions numerically. From this research it appears that mobility cannot explain the pattern of spread of the epidemic fully.
The introduction of the autoregressive process as per [3] to model further residuals has improved this aspect of the model. This term may be reflecting other NPIs, general population awareness and behaviour adjustment or other unmodelled disease effects. However these should be treated as an error term in that they do not aid the understanding of the disease and show deficiencies in this model.
Along with the above, the author intends to investigate the following:
The model assumes that the current reproduction number, \(R_{t,m}\), is a function of the initial reproduction number, \(R_{0,m}\), and changes in mobility over time. It then calculates infections as a function of \(R_{t,m}\) over time, and then, using these infections calculates deaths from the infections based on a distribution of time to death.
Various prior distributions are assumed. The model structure is similar to that in [1] and is briefly documented below. The parameters are estimated jointly using a single hierarchical model covering all provinces. This means that data in different provinces are combined to inform all parameters in the model. As per [1], fitting was done in R using Stan with an adaptive Hamiltonian Monte Carlo sampler.
The model is documented here but is similar to [1]. The model assumes a base reproduction number (\(R_{0,m}\)) for each province (\(m\)) and then it models future values of the reproduction number using mobility indexes as follows:
\(R_{t,m}=R_{0,m}\cdot2\cdot\phi^{-1}(-(\alpha+\alpha_{m}^s)I_{t,m}^{\alpha}-(\beta+\beta_{m}^s)I_{t,m}^{\beta}-\epsilon_{w_m(t),m})\)
Here:
Infections are modelled as:
\(c_{t,m}=S_{t,m}R_{t,m}\sum_{\tau=0}^{t-1}c_{\tau,m}g_{t-\tau}\) where \(S_{t,m}=1 - \frac{\sum_{i=0}^{t-1}c_{i,m}}{N_{m}}\).
Infections, \(c_{t,m}\) at time \(t\) are a function of proportion of population not yet infected (\(S_{t,m}\)), the reproduction number (\(R_{t,m}\)) and infections prior to that \(c_{\tau,m}\) as well as an infectiousness curve \(g_{t-\tau}\). \(N_m\) is the population in province \(m\).
Deaths, \(d_{t,m}\) are modelled as:
\(d_{t,m}=ifr_{m}^*\sum_{\tau=0}^{t-1}c_{\tau,m}\pi_{t-\tau}\)
Here:
It is assumed that COVID-19 deaths are a proportion of excess deaths (\(\psi_m\)). We calculate weekly excess deaths as:
Reported deaths \(D_{t,m}\) are assumed to have the following distribution:
\(D_{t,m} \sim Negative\ Binomial(d_{t,m},d_{t,m}+ \frac{{d}_{t,m}^2}{\phi})\)
If \(Y \sim N(\mu,\sigma)\) then we define \(N^{+}\) to mean the distribution of \(|Y| \sim N^{+}(\mu,\sigma)\).
We assume that:
\(\phi \sim N^{+}(0,5)\)
Then: \(d_{t,m}=E(D_{t,m})\)
The following assumptions are taken as is from [1] except where indicated. These are also very similar to the more recent [17].
We add random noise to the IFR as follows:
\(ifr_{m}^*=ifr_{m}\cdot N(1,0.1)\)
\(\alpha\) and \(\beta\) are distributed as follows:
\(\alpha \sim N(0,0.5)\)
\(\beta \sim N^{+}(0,1)\)
The above distribution for \(\beta\) has been increased to reflect [18] which indicated an effect of mask-wearing. In this paper a relative risk of 0.56 is indicated for mask-wearing in non-health-care settings. The above prior assumption would indicate a 0.62 expected relative risk. \(\beta\) is not a parameter in the model used in [1].
Then for the provincial specific index effects we use:
\(\alpha_{m}^s \sim N(0,\gamma^{\alpha})\) with \(\gamma^{\alpha} \sim N^{+}(0,0.5)\)
\(\beta_{m}^s \sim N(0,\gamma^{\beta})\) with \(\gamma^{\beta} \sim N^{+}(0,0.5)\)
\(\beta_{m}^s\) is a parameter in the model used in [1].
The \(R_{0,m}\) are defined to be distributed normally as follows:
\(R_{0,m} \sim N(3.28,\kappa)\) with \(\kappa \sim N^{+}(0,0.5)\)
\(\epsilon_{w_m(t),m}\), the weekly province specific effect above is as described in [3]:
Infectiousness follows this distribution:
\(g \sim Gamma(6.5,0.62)\)
Infectiousness / Serial Interval
Time to death follows this distribution:
\(\pi \sim Gamma(5.1,0.86)+Gamma(17.8,0.45)\)
The distribution of time to death is plotted below.
Distribution of Time to Death since Infection
The above implies an average time to death of 23 days.
Death and case data were used from [4]. This data set contains provincial case and death data as released by various provinces.
The only adjustments to the data relates to large numbers of deaths reported in Ontario on 2 and 3 October 2020 “due to a data review”. 111 of the deaths reported on these two dates are deaths that occurred during the prior spring and summer (see [19] and [20]). Based on this these deaths were removed from 2 and 3 October and added back in prior days in proportion to deaths reported up un till 30 September 2020. The net effect is no change in reported deaths, but a peak in October is avoided which would have biased calibration of the model.
Provinces are grouped as follows. The province grouping “Territories” are not modelled as there is too few reported deaths to date to model.
| Province | Province Grouping |
|---|---|
| Alberta | Alberta |
| British Columbia | British Columbia |
| Manitoba | Manitoba |
| New Brunswick | Maritime Provinces |
| Newfoundland and Labrador | Maritime Provinces |
| Nova Scotia | Maritime Provinces |
| Nunavut | Territories |
| Northwest Territories | Territories |
| Ontario | Ontario |
| Prince Edward Island | Maritime Provinces |
| Quebec | Quebec |
| Saskatchewan | Saskatchewan |
| Yukon | Territories |
This paper uses IFRs per Levin et al. [12]. The IFR (\(ifr_{m}\)) for each province was calculated using the output of the squire R package [21] for Canada. It produces age-specific infection attack rates (IAR). The projection was done using the default parameters for Canada and the resultant attack rate (\(a_{x}\)) for each 5-year age band was obtained (\(x\)).
The IFR formula from [12] was used to calculate an IFR (\(ifr_{x}\) for each age band. For 80+ the age 85 was used. The attack rate and IFR were used together with the per age band IAR and these were applied to provincial populations [22] to calculate an average IFR for each province based on the province’s age profile.
\(ifr_{m}=\frac{\sum_{x}N_{x,m} \cdot a_{x} \cdot ifr_{x} }{\sum_{x}N_{x,m}}\)
Here \(N_{x,m}\) is the population in a particular province (\(m\)) and age band (\(x\)).
Below we tabulate the resultant \(ifr_{m}\):
| Province | IFR |
|---|---|
| Alberta | 0.73% |
| British Columbia | 1.02% |
| Manitoba | 0.87% |
| Maritime Provinces | 1.11% |
| Ontario | 0.96% |
| Quebec | 1.06% |
| Saskatchewan | 0.89% |
The differences between provinces reflect the different age profiles in those provinces as per [22].
Google has released aggregated mobility data for various countries and for sub-regions in those countries. These data are generated from devices that have enabled the Location History in Google Maps. This feature is available both on Android and iOS devices but is off by default.
For Canada, these data contain the mobility indexes for each province. These are described in [5] as follows:
These measure changes in mobility relative to a baseline established before the epidemic. For example, -30% implies a 30% reduction in mobility from pre-COVID-19 mobility.
As per [8] these data were combined into an average mobility index for each province which was an average of all mobility indexes excluding:
In [1] three indexes were used (Residential, Transit and the rest). This was reduced for this paper due to limited data.
This paper has set out to show how a Bayesian model can be fitted to the Canadian data. From the process it becomes clear that there remains significant uncertainty with all matters relating this epidemic. It is therefore likely that the model will not be accurate.
This paper has however attempted to allow for uncertainty using the Bayesian approach here which results in at least some distribution of possible results, some of which are definitely catastrophic and some of which are less severe.
It is hoped that this is a useful contribution to the ongoing research on the epidemic.
[1] M. Vollmer et al., “Report 20: A sub-national analysis of the rate of transmission of COVID-19 in Italy,” Imperial College London, 2020 [Online]. Available: https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-20-italy/
[2] T. Mellan et al., “Report 21: Estimating COVID-19 cases and reproduction number in Brazil,” Imperial College London, 2020 [Online]. Available: https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-21-brazil/
[3] H. Unwin et al., “Report 23: State-level tracking of COVID-19 in the United States,” Imperial College London, 2020 [Online]. Available: https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-23-united-states/
[4] I. Berry, J.-P. R. Soucy, A. Tuite, and D. Fisman, “Open access epidemiologic data and an interactive dashboard to monitor the COVID-19 outbreak in Canada,” Canadian Medical Association Journal, vol. 192, no. 15, pp. E420–E420, Apr. 2020, doi: 10.1503/cmaj.75262. [Online]. Available: https://www.cmaj.ca/content/192/15/E420
[5] Google LLC, “Google COVID-19 community mobility reports.” 2020 [Online]. Available: https://www.google.com/covid19/mobility/
[6] A. Karaivanov, S. E. Lu, H. Shigeoka, C. Chen, and S. Pamplona, “Face Masks, Public Policies and Slowing the Spread of COVID-19: Evidence from Canada,” medRxiv, p. 2020.09.24.20201178, Oct. 2020, doi: 10.1101/2020.09.24.20201178. [Online]. Available: https://www.medrxiv.org/content/10.1101/2020.09.24.20201178v2. [Accessed: 31-Oct-2020]
[7] R Core Team, R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing, 2019 [Online]. Available: https://www.R-project.org/
[8] P. Nouvellet et al., “Report 26: Reduction in mobility and COVID-19 transmission,” Imperial College London, 2020 [Online]. Available: https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-26-mobility-transmission/
[9] G. E. P. Box, “Robustness in the strategy of scientific model building,” in Robustness in statistics, Elsevier, 1979, pp. 201–236 [Online]. Available: https://doi.org/10.1016/b978-0-12-438150-6.50018-2
[10] N. N. Taleb, Y. Bar-Yam, and P. Cirillo, “On Single Point Forecasts for Fat-Tailed Variables,” 31-Jul-2020. [Online]. Available: http://arxiv.org/abs/2007.16096. [Accessed: 26-Oct-2020]
[11] P. Cirillo and N. N. Taleb, “Tail risk of contagious diseases,” Nature Physics, vol. 16, no. 6, pp. 606–613, May 2020, doi: 10.1038/s41567-020-0921-x. [Online]. Available: https://www.nature.com/articles/s41567-020-0921-x
[12] A. T. Levin, G. Meyerowitz-Katz, N. Owusu-Boaitey, K. B. Cochran, and S. P. Walsh, “Assessing the age specificity of infection fatality rates for COVID-19: Systematic review, Meta-Analysis, and public policy implications,” Jul. 2020, doi: 10.1101/2020.07.23.20160895. [Online]. Available: https://doi.org/10.1101/2020.07.23.20160895
[13] G. Meyerowitz-Katz and L. Merone, “A systematic review and meta-analysis of published research data on COVID-19 infection-fatality rates” [Online]. Available: https://www.medrxiv.org/content/10.1101/2020.05.03.20089854v3
[14] R. Verity et al., “Estimates of the severity of coronavirus disease 2019: A model-based analysis,” The Lancet Infectious Diseases, vol. 20, no. 6, pp. 669–677, Jun. 2020, doi: 10.1016/s1473-3099(20)30243-7. [Online]. Available: https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30243-7/fulltext
[15] N. Brazeau et al., “Report 34: COVID-19 infection fatality ratio: Estimates from seroprevalence,” Imperial College London, 34, Oct. 2020 [Online]. Available: https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-34-ifr/. [Accessed: 30-Oct-2020]
[16] S. Flaxman et al., “Report 13: Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries,” Imperial College London, 2020 [Online]. Available: https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-13-europe-npi-impact/
[17] H. J. T. Unwin et al., “State-level tracking of COVID-19 in the United States,” medRxiv, p. 2020.07.13.20152355, Oct. 2020, doi: 10.1101/2020.07.13.20152355. [Online]. Available: https://www.medrxiv.org/content/10.1101/2020.07.13.20152355v2. [Accessed: 01-Nov-2020]
[18] D. K. Chu et al., “Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: A systematic review and meta-analysis,” The Lancet, vol. 395, no. 10242, pp. 1973–1987, Jun. 2020, doi: 10.1016/S0140-6736(20)31142-9. [Online]. Available: https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)31142-9/fulltext
[19] G. Rodrigues, “Ontario reports new record of 732 coronavirus cases, adds 76 more deaths due to data cleanup,” Global News. [Online]. Available: https://globalnews.ca/news/7373691/ontario-coronavirus-cases-october-2-covid19/. [Accessed: 01-Nov-2020]
[20] R. Rocca, “Ontario reports 653 coronavirus cases after record number of tests completed,” Global News. [Online]. Available: https://globalnews.ca/news/7376209/ontario-coronavirus-cases-oct-3-covid19/. [Accessed: 01-Nov-2020]
[21] P. Walker et al., “Report 12: The global impact of COVID-19 and strategies for mitigation and suppression,” Imperial College London, 2020 [Online]. Available: https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-12-global-impact-covid-19/
[22] S. Canada, “Population estimates on July 1st, by age and sex.” Government of Canada, 30-Oct-2020 [Online]. Available: https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=1710000501. [Accessed: 30-Oct-2020]